Reduction principle for partial functional differential equation without compactness
DOI:
https://doi.org/10.58997/ejde.2023.39Keywords:
Functional differential equations; quasi-compact semigroup; variation of constants formula; Stepanov-almost automorphic function; almost automorphic solution; almost periodic solutionAbstract
This article establishes a reduction principle for partial functional differential equation without compactness of the semigroup generated by the linear part. Under conditions more general than the compactness of the C0-semigroup generated by the linear part, we establish the quasi-compactness of the C0-semigroup associated to the linear part of the partial functional differential equation. This result allows as to construct a reduced system that is posed by an ordinary differential equation posed in a finite dimensional space. Through this result we study the existence of almost automorphic and almost periodic solutions for partial functional differential equations. For illustration, we study a transport model.
For more information see https://ejde.math.txstate.edu/Volumes/2023/39/abstr.html
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Copyright (c) 2023 Meryem El Attaouy, Khalil Ezzinbi, Gaston Mandata ˜N'Guerekata
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